hrmm well x - 5 > 0 so x>5 which is correct
but x + 4 >0 turning to x>-4 isn't right it should be x<-4 how do I get that answer?

you just change it to that answer. sometimes when solving inequalities, the signs end up turning the wrong way, even though you did nothing wrong in the algebraic manipulation. that's why you always check your answers with these, so you know you have your signs pointing the right way, as you did. now just draw those solutions on a number line